Physics - Current Electricity Question with Solution | TestHub

The bridge is balanced: 2/4 = 3/6, so the 5 Ω resistor carries no current and $R_{eq}=(2+4)\Vert (3+6)=6\Vert 9=3.6\Omega$

(A) Short the 4 Ω: the network reduces to $R=6\Vert \left(\frac{2\times 5}{2+5}+3\right)=6\Vert \frac{31}{7}=\frac{186}{73}\approx 2.55\Omega <3.6\Omega$ so the battery current increases. Correct.

(B) With 4 Ω shorted the bridge is no longer balanced, so current through the 5 Ω resistor rises from zero. Correct.

(C) Short the 5 Ω: $R=(2\Vert 4)+(3\Vert 6)=\frac{4}{3}+2=\frac{10}{3}\Omega <3.6\Omega$ so the current increases, not decreases. Wrong.

(D) Short the 3 Ω: $R=2\Vert \left(4+\frac{6\times 5}{6+5}\right)=2\Vert \frac{74}{11}\approx 1.54\Omega <3.6\Omega$ so the current increases. Wrong.

Hence (A) and (B).